From efaabc3e2ffa68de98d48821d6d338500f2cd093 Mon Sep 17 00:00:00 2001
From: CarlosZoft <62192072+CarlosZoft@users.noreply.github.com>
Date: Tue, 15 Feb 2022 14:27:02 -0300
Subject: [PATCH] feat : add modular_inverse_simple

---
 math/modular_inverse_simple.cpp | 69 +++++++++++++++++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 math/modular_inverse_simple.cpp

diff --git a/math/modular_inverse_simple.cpp b/math/modular_inverse_simple.cpp
new file mode 100644
index 000000000..b0df7d02b
--- /dev/null
+++ b/math/modular_inverse_simple.cpp
@@ -0,0 +1,69 @@
+/**
+ * @file
+ * @brief simple implementation of adaption modular multiplicative inverse
+ * algorithm
+ *
+ * @details
+ * this algorithm calculate the modular inverse iteratively
+ *
+ * @ref
+ * https://en.wikipedia.org/wiki/Modular_multiplicative_inverse
+ */
+
+#include <cassert>
+#include <iostream>
+
+// Macro
+#define Key(A)       (A)
+#define module(A, B) (Key(A) % Key(B))
+
+using namespace std;
+
+/**
+ * @brief Function imod
+ *  Responsible for calculating the modular inverse from x % y
+ * @param x number
+ * @param y number
+ * @returns the modular inverse
+ */
+int imod(int x, int y) {
+    int aux, itr = 0;
+
+    do {  // run the algorithm while not find the inverse
+        aux = y * itr + 1;
+        itr++;
+    } while (module(aux, x));  // while module(aux, x) is different of zero
+
+    return aux / x;
+}
+
+/**
+ * @brief Some test cases
+ * @returns void
+ */
+static void test() {
+    cout << "First case testing... \n";
+    // for a = 3 and b = 11 return 4
+    cout << imod(3, 11) << endl;
+    assert(imod(3, 11) == 4);
+    cout << "\nPassed!\n";
+
+    cout << "Second case testing... \n";
+    // for a = 3 and b = 26 return 9
+    assert(imod(3, 26) == 9);
+    cout << "\nPassed!\n";
+
+    cout << "Third case testing... \n";
+    // for a = 7 and b = 26 return 15
+    assert(imod(7, 26) == 15);
+    cout << "\nPassed!\n";
+
+    cout << "\nAll test cases have successfully passed!\n";
+}
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run tests implementations
+};